## Learning Outcomes

After studying this article, you will be able to explain the structure and purpose of time series analysis in management accounting. You will be able to identify and describe the components of time series data, including trends and seasonal variations, and apply simple moving averages to identify these elements. You will also be able to forecast future values using additive and multiplicative models, preparing you thoroughly for ACCA PM exam requirements.

## ACCA Performance Management (PM) Syllabus

For ACCA Performance Management (PM), you are required to understand forecasting techniques as a key analytical tool for budgeting and control. This article focuses on time series specifically. Ensure you can:

- Describe the components of a time series: trend, seasonality, cycle, and random variation.
- Calculate and interpret moving averages to identify trends.
- Isolate and interpret seasonal variations using both additive and multiplicative models.
- Use time series analysis to forecast future values for budgeting purposes.
- Discuss the strengths and weaknesses of time series methods for forecasting.

## Test Your Knowledge

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, look more closely at that area during your revision._

1. What information does a moving average provide when analysing a time series of monthly sales data?
2. If sales are higher every December, what aspect of a time series explains this?
3. What is the main difference between the additive and multiplicative models when accounting for seasonality?
4. Give one limitation of using time series analysis for forecasting in a fast-changing business environment.

## Introduction

Forecasting using time series analysis is a fundamental skill for budgeting, planning, and performance evaluation in management accounting. Time series analysis uses historical data to project future values, based on identified patterns. The ACCA PM exam may test your ability to calculate moving averages, isolate components such as trends and seasonal variations, and interpret or forecast figures using these techniques.

> **Key Term: time series**
> A sequence of data points measured at regular time intervals, such as monthly sales figures, where the variable of interest is tracked over time.

### COMPONENTS OF A TIME SERIES

A time series can usually be broken down into four main components:

- **Trend (T):** The long-term direction in the data (upward, downward, or flat).
- **Seasonal Variation (S):** Predictable changes that repeat over a fixed period, often within a year.
- **Cyclical Variation (C):** Fluctuations with a pattern lasting more than one year (linked to economic cycles).
- **Random Variation (R):** Irregular, unpredictable factors with no consistent pattern.

Most ACCA PM questions focus on trend and seasonality.

> **Key Term: trend**
> The fundamental long-term movement, either upward or downward, in a time series after removing short-term fluctuations.
> **Key Term: seasonal variation**
> Regular, predictable changes in a time series that recur at the same period each cycle, such as higher sales every summer.

### IDENTIFYING THE TREND USING MOVING AVERAGES

A moving average is calculated by averaging a fixed number of consecutive values from the time series, producing a series of averages that 'smooths' short-term fluctuations, making the trend easier to see.

![Moving-average trend extraction from time series data using odd-span averaging and even-span double centring to align a smoothed trend series.](https://static.pastpaperhero.com/images/acca-pm-forecasting-techniques-time-series-trend-seasonality-moving-averages_00.png)

_Time-series smoothing procedure distinguishes centred odd-period averages from even-period double-centred averages before producing the aligned trend series._

> **Key Term: moving average**
> The average of a set span of consecutive data points in a time series, used to highlight the trend by removing the effect of seasonality and irregular events.

### Worked Example 1.1

A company records its monthly sales (in \$000):
Jan: 120, Feb: 140, Mar: 135, Apr: 160, May: 155, Jun: 145.

Calculate the 3-month moving averages for February to May.

> **Answer:**
> The 3-month moving averages are:
>
> - Feb: (120 + 140 + 135) / 3 = 131.7
> - Mar: (140 + 135 + 160) / 3 = 145.0
> - Apr: (135 + 160 + 155) / 3 = 150.0
> - May: (160 + 155 + 145) / 3 = 153.3

### Interpreting Moving Averages

The moving averages remove irregular and seasonal effects, leaving a clearer trend. The trend value for any given period is usually aligned with the centre of the average (e.g., Mar for a 3-month moving average). For even periods (e.g., 4-month moving average), double-centred moving averages are used.

> **Revision Tip:**
> If the exam asks you to calculate a moving average, always check whether you are using an odd or even number of periods. For an even number, you must centre the average between periods.

### ISOLATING SEASONAL VARIATION

Once the fundamental trend is revealed by moving averages, the seasonal variation can be calculated as the difference between the actual value and the trend value for the same period.

### Additive and Multiplicative Models

There are two ways to model seasonality:

- **Additive model:** Assumes the seasonal effect is constant each period—actual = trend + seasonal variation.
- **Multiplicative model:** Assumes the seasonal effect is a percentage of the trend—actual = trend × seasonal factor.

> **Key Term: additive model**
> A time series model where actual values are the sum of the trend and seasonal variation for each period.
> **Key Term: multiplicative model**
> A time series model where actual values are the product of the trend and a seasonal factor for each period.

### Worked Example 1.2

The computed trend value for July is 200 units. The actual sales in July are 220 units.

a) Calculate the seasonal variation using the additive model.
b) Calculate the seasonal index (as a percentage) using the multiplicative model.

> **Answer:**
> a) Additive: Seasonal variation = Actual – Trend = 220 – 200 = **20 units**
> b) Multiplicative: Seasonal index = Actual / Trend = 220 / 200 = **1.10** (or 110%)

### Using Seasonal Variations for Forecasts

Once you have isolated the trend and seasonal variation, you can forecast future periods—for example, by projecting the trend forward and adding the average seasonal variation for the relevant month or quarter.

### Worked Example 1.3

You have calculated the following trend forecast for Q1 20X5 as 500 units, and the average seasonal variation for Q1 is +40 units (additive model). Forecast the expected sales for Q1 20X5.

> **Answer:**
> Forecast sales = Trend + Seasonal variation = 500 + 40 = **540 units**

If the multiplicative model is used and the seasonal index for Q1 is 1.08, the forecast sales would be 500 × 1.08 = **540 units**.

### ADVANTAGES AND LIMITATIONS OF TIME SERIES ANALYSIS

### Benefits

- Identifies fundamental patterns for better forecasts.
- Useful when trends and seasonality are stable year to year.
- Assists in planning, budgeting, and resource allocation.

### Limitations

- Forecasts assume past patterns continue, which may not hold in a changing environment.
- Does not predict the impact of exceptional events, like economic shocks.
- The method is less reliable if data is highly random or has irregular cycles.
- Requires sufficient and accurate historical data.

> **Exam Warning:**
> Do not forget to check for changes in seasonality or trend: exam questions may include a change in business conditions. Forecasts using time series are only valid if patterns are expected to continue similarly into the future.

## Summary

Time series analysis provides a structured approach to breaking down historical data into trend and seasonal components. Moving averages help detect the fundamental trend, while the difference between the actual and trend values reveals seasonal variation. Both additive and multiplicative models are commonly used for seasonal adjustment and forecasting. However, always consider whether the assumptions of consistent trend and seasonality are reasonable in your business context.

## Key Point Checklist

_This article has covered the following key knowledge points:_

- Identify and explain the four components of a time series.
- Calculate and interpret moving averages to reveal trends.
- Isolate and interpret seasonal variation using additive and multiplicative models.
- Use time series analysis to forecast future values for budgeting.
- Recognise strengths and limitations of time series forecasting methods.

## Key Terms and Concepts

- time series
- trend
- seasonal variation
- moving average
- additive model
- multiplicative model


Forecasting techniques - Time series: trend, seasonality, moving averages